کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4604955 1337533 2016 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimal designs of positive definite kernels for scattered data approximation
ترجمه فارسی عنوان
طرح های بهینه از هسته های قطعی مثبت برای تقریب اطلاعات پراکنده
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

In this article, we study the optimal designs of the positive definite kernels for the high-dimensional interpolation. We endow the Sobolev spaces with the probability measures induced by the positive definite kernels such that the kernel-based estimators can be solved to maximize the kernel-based probabilities conditioned on the observed data. In the practical implementations, we have many choices of the positive definite kernels to construct the kernel basis such as the Gaussian kernels with various shape parameters; hence we have an open problem what the optimal kernels are. The kernel-based probabilities provide a novel way to search the optimal kernels for the observed data. Combining with the statistical techniques such as the maximum likelihood estimation, we can solve the optimal shape parameters of the Gaussian kernels by the kernel-based probabilities even though the classical kernel-based methods cannot achieve the uncertain data.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 41, Issue 1, July 2016, Pages 214–236
نویسندگان
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